3. Unit Circle

Find exact values or expressions for sin A, cos A, and tan A. See Example 1.

Determine whether each statement is true or false. If false, tell why.tan 60° ≥ cot 40°

Determine whether each statement is true or false. If false, tell why.csc 22° ≤ csc 68°

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C.Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1.a = 5, b = 12

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C.Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1.a = 6, c = 7

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C.Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1.b = 8, c = 11

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C.Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1.a = √2, c = 2

In Exercises 17–20, θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, sec θ, and cot θ. Where necessary, rationalize denominators.__sin θ = 6, cos θ = √137 7

In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ.sin θ = 6/7

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.sin 45°

In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ.__sin θ = √398

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.tan 25.4°

In Exercises 28–29, find a cofunction with the same value as the given expression.sin 70°

In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator.sin² 𝜋 + cos² 𝜋 10 10

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.cos(θ + 20°)